Question

oscar has $3,000 in an account that earns 6% interest compounded annually. to the nearest cent, how much interest will he earn in 1 year? use the formula $b = p(1 + r)^t$, where $b$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years.

Explanation:

Step1: Identify given values

Principal \( p = 3000 \), rate \( r = 6\% = 0.06 \), time \( t = 1 \).

Step2: Calculate balance \( B \)

Using formula \( B = p(1 + r)^t \), substitute values:
\( B = 3000(1 + 0.06)^1 = 3000 \times 1.06 = 3180 \).

Step3: Find interest earned

Interest = \( B - p = 3180 - 3000 = 180 \).

Answer:

180.00